Problem: Multiply the following complex numbers: $({-4-5i}) \cdot ({-4-i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-4-5i}) \cdot ({-4-i}) = $ $ ({-4} \cdot {-4}) + ({-4} \cdot {-1}i) + ({-5}i \cdot {-4}) + ({-5}i \cdot {-1}i) $ Then simplify the terms: $ (16) + (4i) + (20i) + (5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 16 + (4 + 20)i + 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 16 + (4 + 20)i - 5 $ The result is simplified: $ (16 - 5) + (24i) = 11+24i $